Solving for the RPM of a Malfunctioning Motor

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To determine the rotational speed of the malfunctioning motor, the operational motor runs at 3600 rpm, and beats are heard every 21 seconds, indicating a frequency difference. The formula for beat frequency is derived from the difference in rotational speeds, where the frequency of beats is equal to the difference in the two motors' speeds. Given that one motor completes one additional rotation in the time interval of 21 seconds, calculations reveal that the malfunctioning motor's speed can be expressed as 3600 rpm plus the difference calculated from the beat frequency. The discussion emphasizes the need for a correct formula to relate the rotational speeds and the observed beat frequency. Understanding this relationship is crucial for solving the problem accurately.
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Homework Statement


Suppose you're operating a machine with two motors. If the two motors are not operating at the same rpm, you will hear a periodic variation in the intensity of the sound-that is, beats. Suppose the tachometer that indicates the rotation rate of one motor is malfunctioning. The operational one shows 3600 rpm. You hear a beat every 21 s. You are certain the other motor is running fast.

What is its rotational speed in rpm?

Homework Equations


w1-w2 is the frequency of amplitude change (according to the textbook).

3. Attempt at solution
delta_w = 2pi/T = w1-w2
w1 - 2pi/T = w2

w2 is not valid (given that I have converted all units to standard and back into rpm). So I think my formula isn't valid. Can someone derive a correct one please? Thanks.
 
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akan said:

Homework Statement


Suppose you're operating a machine with two motors. If the two motors are not operating at the same rpm, you will hear a periodic variation in the intensity of the sound-that is, beats. Suppose the tachometer that indicates the rotation rate of one motor is malfunctioning. The operational one shows 3600 rpm. You hear a beat every 21 s. You are certain the other motor is running fast.

What is its rotational speed in rpm?

Homework Equations


w1-w2 is the frequency of amplitude change (according to the textbook).

3. Attempt at solution
delta_w = 2pi/T = w1-w2
w1 - 2pi/T = w2

w2 is not valid (given that I have converted all units to standard and back into rpm). So I think my formula isn't valid. Can someone derive a correct one please? Thanks.

How many times has one motor turned in 21 seconds?

If during the beat the "faster" one precessed such that you discrened a "beat" wouldn't that mean that the faster one - over that time - rotated 1 more complete time than the other?
 
>> How many times has one motor turned in 21 seconds?
The first one rotated 3600 rpm * m/60s * 21s times. I don't know about the second one since it's the one I need to find.

>> If during the beat the "faster" one precessed such that you discerned a "beat" wouldn't that mean that the faster one - over that time - rotated 1 more complete time than the other?

Why would it be "1" more complete time than the other? How do I know how many more times it rotated? How is this tied into the formula? Thanks.
 
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